Allows to estimate Treynor-Mazuy or Merton-Henriksson market timing model. The Treynor-Mazuy model is essentially a quadratic extension of the basic CAPM. It is estimated using a multiple regression. The second term in the regression is the value of excess return squared. If the gamma coefficient in the regression is positive, then the estimated equation describes a convex upward-sloping regression "line". The quadratic regression is: $$R_{p}-R_{f}=\alpha+\beta (R_{b} - R_{f})+\gamma (R_{b}-R_{f})^2+ \varepsilon_{p}$$ \(\gamma\) is a measure of the curvature of the regression line. If \(\gamma\) is positive, this would indicate that the manager's investment strategy demonstrates market timing ability.
MarketTiming(Ra, Rb, Rf = 0, method = c("TM", "HM"))
| Ra | an xts, vector, matrix, data frame, timeSeries or zoo object of the asset returns |
|---|---|
| Rb | an xts, vector, matrix, data frame, timeSeries or zoo object of the benchmark asset return |
| Rf | risk free rate, in same period as your returns |
| method | used to select between Treynor-Mazuy and Henriksson-Merton models. May be any of:
By default Treynor-Mazuy is selected |
| … | any other passthrough parameters |
The basic idea of the Merton-Henriksson test is to perform a multiple regression in which the dependent variable (portfolio excess return and a second variable that mimics the payoff to an option). This second variable is zero when the market excess return is at or below zero and is 1 when it is above zero: $$R_{p}-R_{f}=\alpha+\beta (R_{b}-R_{f})+\gamma D+\varepsilon_{p}$$ where all variables are familiar from the CAPM model, except for the up-market return \(D=max(0,R_{b}-R_{f})\) and market timing abilities \(\gamma\)
J. Christopherson, D. Carino, W. Ferson. Portfolio Performance Measurement and Benchmarking. 2009. McGraw-Hill, p. 127-133. J. L. Treynor and K. Mazuy, "Can Mutual Funds Outguess the Market?" Harvard Business Review, vol44, 1966, pp. 131-136 Roy D. Henriksson and Robert C. Merton, "On Market Timing and Investment Performance. II. Statistical Procedures for Evaluating Forecast Skills," Journal of Business, vol.54, October 1981, pp.513-533
data(managers) MarketTiming(managers[,1], managers[,8], Rf=.035/12, method = "HM")#> Alpha Beta Gamma #> HAM1 to SP500 TR 0.008275839 0.4555824 -0.1344417MarketTiming(managers[80:120,1:6], managers[80:120,7], managers[80:120,10])#> Alpha Beta Gamma #> HAM1 to EDHEC LS EQ -0.0005755802 1.3121058 -0.405150 #> HAM2 to EDHEC LS EQ -0.0003616789 0.4370998 8.520620 #> HAM3 to EDHEC LS EQ -0.0058148518 1.1898242 11.913786 #> HAM4 to EDHEC LS EQ -0.0055113742 2.0616524 18.797340 #> HAM5 to EDHEC LS EQ 0.0005125284 1.0703704 -5.077881 #> HAM6 to EDHEC LS EQ 0.0003590925 1.2711094 -7.443428MarketTiming(managers[80:120,1:6], managers[80:120,8:7], managers[80:120,10], method = "TM")#> Alpha Beta Gamma #> HAM1 to SP500 TR 0.0048833318 0.5970167 -0.2801650 #> HAM2 to SP500 TR 0.0050694247 0.1190405 -0.5000263 #> HAM3 to SP500 TR 0.0032110848 0.5272982 -0.6645684 #> HAM4 to SP500 TR 0.0094634771 0.8779523 -0.8155100 #> HAM5 to SP500 TR 0.0087234498 0.2869943 -2.7728051 #> HAM6 to SP500 TR 0.0048031173 0.2902262 0.6910898 #> HAM1 to EDHEC LS EQ -0.0005755802 1.3121058 -0.4051500 #> HAM2 to EDHEC LS EQ -0.0003616789 0.4370998 8.5206196 #> HAM3 to EDHEC LS EQ -0.0058148518 1.1898242 11.9137857 #> HAM4 to EDHEC LS EQ -0.0055113742 2.0616524 18.7973395 #> HAM5 to EDHEC LS EQ 0.0005125284 1.0703704 -5.0778814 #> HAM6 to EDHEC LS EQ 0.0003590925 1.2711094 -7.4434281